Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(2 e^{5\pi i / 3}) \cdot (5 e^{\pi i / 6})$ (Your current answer will be plotted in orange.)
Explanation: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $2 e^{5\pi i / 3}$ ) has angle $\frac{5}{3}\pi$ and radius $2$ The second number ( $5 e^{\pi i / 6}$ ) has angle $\frac{1}{6}\pi$ and radius $5$ The radius of the result will be $2 \cdot 5$ , which is $10$ The angle of the result is $\frac{5}{3}\pi + \frac{1}{6}\pi = \frac{11}{6}\pi$ The radius of the result is $10$ and the angle of the result is $\frac{11}{6}\pi$.